Purdal

Purdal is a unit of measure for musical intervals, suggested by Tútim Dennsuul, which is the Ditave (2/1, the 'Octave') divided into 9900 equal parts. The Purdals are shown as a reliable and very consistent to idealize any musical system, whether just or temperate.
The purpose that it have is for the need of precise with better quality in its presentation, those 'EDDs' who have a quantity equal to a prime number of intervals and systems until 990 steps per Ditave, only requiring 2 decimals for a basic precision. The 12-EDD contains 825 Purdals in each semitone; Each Purdal is equivalent to 4/33 of a Cent (0.12 Cents), and 1 Cent is 8.25 Purdals.

The ditaved Purdal is divisible by: 2, 3, 4, 5, 6, 9, 10, 11, 12, 15, 18, 20, 22, 25, 30, 33, 36, 44, 45, 50, 55, 60, 66, 75, 90, 99, 100, 110, 132, 150, 165, 180, 198, 220, 225, 275, 300, 330, 396, 450, 495, 550, 660, 825, 900, 990, 1100, 1650, 1980, 2475, 3300 & 4950 exact parts.



The table below show us uniquely the translation of the Purdal values without decimals, to the simple Cent equivalence,in some harmonic ratios for comparisson:

The Purdal symbol

Harmonic (until the 63º)	Purdal entire value	Cent equivalence
2/1	9900	1200
3/2	5791	701.93
5/4	3187	386.30
7/4	7993	968.84
9/8	1682	203.87
11/8	4548	551.27
13/8	6934	840.48
15/8	8978	1088.24
17/16	866	104.96
19/16	2454	297.45
21/16	3884	470.78
23/16	5183	628.24
25/16	6374	772.60
27/16	7473	905.81
29/16	8494	1029.57
31/16	9447	1145.09
33/32	440	53.3
35/32	1280	155.15
37/32	2074	251.39
39/32	2825	342.42
41/32	3540	429.09
43/32	4220	511.51
45/32	4869	590.18
47/32	5490	665.45
49/32	6086	737.69
51/32	6657	806.90
53/32	7206	873.45
55/32	7735	937.57
57/32	8246	999.51
59/32	8738	1059.15
61/32	9214	1116.84
63/32	9675	1172.72

If you want real values between Purdal sizes and Cents sizes with any ratios, check them with this Purdal calculator.!!'!!!'!!!!'!!!'!!!!'!!!'!!!!'!!!'!!!!'!!!'!!!!'!!!'!!!!'!!!'!!!!'!!!'!!!!'!!!'!!

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This information is included from the Purdal wiki, see purdal/purdal.